Suppose that $f : \mathbb{R}^n \to \mathbb{R}$ is Lipschitz continuous, can we conclude that $$ \int_{[0,1]} (y-x)^T \nabla f(\mu y + (1-\mu )x) \text{d}\mu = f(y) - f(x) $$ where $\int$ stands for Lebesgue integral?
2026-03-27 10:16:58.1774606618
Fundamental theorem of line integral for Lipschitz continuous function
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